As they walked along a red carpet through the rotunda ­under the golden dome, ­Cameron could be seen pointing and nodding at historical displays.

The prime minister did not make any public statement and exited the governor’s office later in the evening without respond­ing to press queries.

Patrick told reporters he had a “great” visit with the Prime Minister.

“We talked about some of the cooperation we have had around the innovation sectors,” the governor said.

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Earlier Monday, Cameron met with President Barack Obama in Washington.

At a White House press conference, Cameron said he looked forward to coming to Boston and paying “tribute” to its people ­after last month’s Boston Marathon attacks, which he called “an appalling outrage.”

“I look forward to going there to pay my tribute to the people of that remarkable city and their courage, and we will always stand with you in the fight against terrorism,” said Cameron.